dorsal/arxiv
View SchemaSeparation of variables in the $A_2$ type Jack polynomials
| Authors | V. B. Kuznetsov, E. K. Sklyanin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9508002 |
| URL | https://arxiv.org/abs/solv-int/9508002 |
| Journal | Various aspects of hypergeometric functions (Japanese) (Kyoto, 1994). Surikaisekikenkyusho Kokyuroku No. 919 (1995), 27-43 |
Abstract
An integral operator $M$ is constructed performing a separation of variables for the 3-particle quantum Calogero-Sutherland (CS) model. Under the action of $M$ the CS eigenfunctions (Jack polynomials for the root system $A_2$) are transformed to the factorized form $\phi(y_1)\phi(y_2)$, where $\phi(y)$ is a trigonometric polynomial of one variable expressed in terms of the ${}_3F_2$ hypergeometric series. The inversion of $M$ produces a new integral representation for the $A_2$ Jack polynomials.
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"abstract": "An integral operator $M$ is constructed performing a separation of variables\nfor the 3-particle quantum Calogero-Sutherland (CS) model. Under the action of\n$M$ the CS eigenfunctions (Jack polynomials for the root system $A_2$) are\ntransformed to the factorized form $\\phi(y_1)\\phi(y_2)$, where $\\phi(y)$ is a\ntrigonometric polynomial of one variable expressed in terms of the ${}_3F_2$\nhypergeometric series. The inversion of $M$ produces a new integral\nrepresentation for the $A_2$ Jack polynomials.",
"arxiv_id": "solv-int/9508002",
"authors": [
"V. B. Kuznetsov",
"E. K. Sklyanin"
],
"categories": [
"solv-int",
"math.QA",
"nlin.SI",
"q-alg"
],
"journal_ref": "Various aspects of hypergeometric functions (Japanese) (Kyoto,\n 1994). Surikaisekikenkyusho Kokyuroku No. 919 (1995), 27-43",
"title": "Separation of variables in the $A_2$ type Jack polynomials",
"url": "https://arxiv.org/abs/solv-int/9508002"
},
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